1. Field of Invention
This invention relates to the circuits used to simulate the electrical characteristics of an inductor and in particular those circuits that can be easily fabricated using standard integrated circuits processing techniques.
2. Description of Related Art
The design of electrical filters and similar applications require the 5 use of resistors (R), capacitors (C), and inductors (L). Practical inductors can not be implemented easily on integrated circuits. The use of passive resistors/capacitors (RC) networks while practical, occupy a relatively large amount of space if implemented in integrated circuits. The RC networks generally are limited to simple applications where a low quality factor (Q) is acceptable.
Active filters incorporating operational amplifiers have very powerful applications since almost any frequency transfer function can be implemented. The bandwidth of these applications, however, will generally be limited to lower frequencies such as in the audio band because of the limited bandwidth of most operational amplifiers.
In FIG. 1A a typical simple series RLC filter is illustrated. The voltage source V.sub.in provides a voltage that is: EQU V.sub.in =V.sub.mix sin(.omega.t).
where
V.sub.max is the maximum value of the voltage of the source; PA1 .omega. is the frequency of the signal in radians per second; PA1 t is the time from the application of the voltage source in seconds. PA1 r.sub.R is the value of the resistor R in ohms (.OMEGA.).
The characteristic of an inductor is that current through the inductor is delayed by .pi./2 radian in phase from the voltage applied to its terminals, the impedance Z.sub.L of the inductor L is: EQU Z.sub.L =j.omega..iota..sub.L
where ##EQU1## .omega. is the frequency of the signal in radians per second.
.iota..sub.L is the value of the inductance of the inductor L in henries.
The impedance Z.sub.R of the resistor R is: EQU Z.sub.R =r.sub.R
where
The impedance Z.sub.c of the Capacitor C is: ##EQU2## where ##EQU3## .omega. is the frequency of the signal in radians per second; C.sub.c is the value of the capacitance of the capacitor C in Farads.
The current i through the network formed by the inductor L, Resistor R, and the Capacitor C is: ##EQU4## and the voltage V.sub.out is: ##EQU5##
FIG. 2 is a plot of the gain (5 V.sup.at /V.sub.in) of the circuit of FIG. 1A as a function of the frequency (Hz) of the voltage source V.sub.in as expressed in decibels (db). Because of nonidealities in the construction of an inductor, a pure inductance is impossible to achieve. A physical inductor is an ideal inductor in series with a resistor. Theoretically the series resistance can be further reduced with advanced IC processing and further circuit optimization.
U.S. Pat. No. 3,448,411 (M. Patterson) teaches a circuit for simulating the electrical characteristics of air core and iron core inductance coils. U.S. Pat. No. 5,093,642 (Mittel) describes a solid state mutually coupled inductor.
U.S. Pat. No. 3,835,399 (R. Holmes) demonstrates a network of operational amplifiers coupled to simulate an inductor.
U.S. Pat. No. 5,235,223 (C. Maple) describes a tunable circuit using synthetic inductors and capacitor multipliers in place of discrete inductive and capacitive elements.